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<b>let </b><font color="Maroon">n</font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">m</font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:31_1_2"/><i><font color="Green">E43</font></i>: 
for <font color="Olive">I</font> being   <a href="vectsp_7.html#M1">Basis</a> of <font color="Maroon">V</font> holds   <a href="card_1.html#K1">Card</a> <font color="Olive">I</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font>
 <b>and </b><br/><a NAME="E2:31_1_2"/><i><font color="Green">E44</font></i>: 
for <font color="Olive">I</font> being   <a href="vectsp_7.html#M1">Basis</a> of <font color="Maroon">V</font> holds   <a href="card_1.html#K1">Card</a> <font color="Olive">I</font> <a href="hidden.html#R1">=</a> <font color="Maroon">m</font>
 ;<br/>

<b>consider </b><font color="Maroon">A</font> being  <a href="finset_1.html#V1">finite</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">V</font><b> such that </b><br/><a NAME="E4:31_1_2"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">A</font> is    <a href="vectsp_7.html#M1">Basis</a> of <font color="Maroon">V</font>
 <b>by </b><i>, </i>;<br/>
<a NAME="E5:31_1_2"/>
(  <a href="card_1.html#K1">Card</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> &amp;  <a href="card_1.html#K1">Card</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">m</font> )
 
<b>by </b><i>, , </i>;<br/>
<b>hence </b><a NAME="E6:31_1_2"/>
<font color="Maroon">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">m</font>
 ;<br/>


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